The phase space method is used in studying a thermo-acoustic heat engine in this paper. The maximum Lyapunov exponent is used to quantify the phase space that is reconstructed from the pressure signal of the thermo-acoustic heat engine. For quantifying the system change, the maximum Lyapunov exponents of the reconstructed pressure phase space trails are calculated. The plot of the maximum Lyapunov exponents versus time is attained. Good agreement between the plot and the evolving process of the real physical phenomenum indicates that the maximum Lyapunov exponents can reflect the state changes of the thermoacoustic heat engine. Published by Elsevier Ltd.